Problem: Simplify the following expression: $r = \dfrac{p^2 + 12p + 20}{p + 2} $
First factor the polynomial in the numerator. $ p^2 + 12p + 20 = (p + 2)(p + 10) $ So we can rewrite the expression as: $r = \dfrac{(p + 2)(p + 10)}{p + 2} $ We can divide the numerator and denominator by $(p + 2)$ on condition that $p \neq -2$ Therefore $r = p + 10; p \neq -2$